Carousels,Zindler curves and the floating body problem

A carousel is a dynamical system that describes the movement of an equilateral linkage in which the midpoint of each rod travels parallel to it. They are closely related to the floating body problem. We prove, using the work of Auerbach, that any figure that floats in equilibrium in every position is drawn by a carousel. Of special interest are such figures with rational perimetral density of the floating chords, which are then drawn by carousels. In particular, we prove that for some perimetral densities the only such figure is the circle, as the problem suggests.     

Pseudorandom properties of prime factors

In this paper we study some pseudo-random properties related to the prime factors of integers. We prove some results concerning the well distribution of the greatest prime factor modulo 4, and give some computational insight on the correlations, which seem to be beyond reach of proof.     

Minimal expansions in redundant number systems: Fibonacci bases and Greedy algorithms

We study digit expansions with arbitrary integer digits in base q (q integer) and the Fibonacci base such that the sum of the absolute values of the digits is minimal. For the Fibonacci case, we describe a unique minimal expansion and give a greedy algorithm to compute it. Additionally, transducers to calculate minimal expansions from other expansions are given. For the case of even integer bases q, similar results are given which complement those given in [6].     

Affine and projective vector fields on spray manifolds

Periodica Mathematica Hungarica -     

Pure Skew Lattices in Rings

Given a ring $R$, let $S\subseteq R$ be a pure multiplicative band that is closed under the cubic join operation $x\nabla y = x+y+yx-xyx-yxy.$ We show that $\left( S,\cdot,\nabla\right) $ forms a pure skew lattice if and only if $S$ satisfies the polynomial identity $\left(xy-yx\right)^{2}z = z\left(xy-yx\right)^{2}$. We also examine properties of pure skew lattices in rings.     

New heuristics for over-constrained flight to gate assignments

We consider the over-constrained Airport Gate Assignment Problem where the number of flights exceed the number of gates available, and where the objectives are to minimize the number of ungated flights and the total walking distances. The problem is formulated as a binary quadratic programming problem. We design a greedy algorithm and use a Tabu Search meta-heuristic to solve the problem. The greedy algorithm minimizes ungated flights while we devise a new neighbourhood search technique, the Interval Exchange Move, which allows us flexibility in seeking good solutions, especially when flight schedules are dense in time. Experiments conducted give good results.     

A flexible and generic approach to dynamic modelling of supply chains

In this paper, we present a new modelling approach for realistic supply chain simulation. The model provides an experimental environment for informed comparison between different supply chain policies. A basic simulation model for a generic node, from which a supply chain network can be built, has been developed using an object-oriented approach. This generic model allows the incorporation of the information and physical systems and decision-making policies used by each node. The object-oriented approach gives the flexibility in specifying the supply chain configuration and operation decisions, and policies. Stochastic simulations are achieved by applying Latin Supercube Sampling to the uncertain variables in descending order of importance, which reduces the number of simulations required. We also present a case study to show that the model is applicable to a real-life situation for dynamic stochastic studies.     

Constructions of economic functions and calculations of marginal rates in DEA using parametric optimization methods

The aim of the paper is to present and substantiate a technique to visualize DEA modelling results without any loss of mathematical rigour. The proposed family of parametric optimization methods allows one to construct an intersection of the multidimensional frontier with a two-dimensional plane determined by any pair of given directions. This approach reduces the efficiency analysis of production units to the investigation of well-known functions in economics. We also propose constructive methods to calculate marginal rates of substitution, marginal rates of transformation and so on.